In this exercise, you are writing some source code files from scratch; two classes, one an abstract class Shape and the second a class Polygon which is a child of the Shape class. You will write a short main function in a main.cpp program file to demonstrate your Polygon class.

Developing the new code and then running the associated main program should demonstrate these learning outcomes:

The ability to understand redefinition of functions by a derived class, originally defined in a base class.

The ability to create virtual and pure virtual functions, understanding the difference between the two and what makes a class Abstract.

The ability to program constructors in a derived class, using their counterparts in the base class.

The ability to override a pure virtual function to create a non$-$abstract child class.

The ability to understand what makes a good virtual or pure virtual function.

Program Requirements

Activity $1)$

This activity requires you to write a new class named Shape$2$D with the following features:

Private member variables:

xcoord: an integer x coordinate to help record position in a $2$D space

ycoord: an integer y coordinate to help record position in a $2$D space

Public member functions:

Default constructor setting xcoord and ycoord to $0$

Constructor with $2$ parameters for xcoord and ycoord

A pure virtual function for calculating Area

In the main function, you should attempt to create an object of type Shape$2$D and record the error message that you get from the compiler. Explain in a comment what is causing this error, as it relates to the pure virtual function for Area.

Activity $2)$

This activity requires you to write a new class named Polygon which inherits $($using public inheritance, which will be our default$)$ from the Shape$2$D class, with the following features:

Private member variables:

width: an integer width

height: an integer height

Public member functions:

Default constructor setting width and height to $0.$

Constructor with $4$ parameter for width, height, xcoord and ycoord. Remember to use the constructor of Shape$2$D to assign its private members.

A virtual function for calculating Area, overriding the pure virtual function definition from Shape$2$D$.$

In the main function, you should attempt to create an object of type Polygon. Test the area function to ensure it is working properly.

Activity $3)$

Suppose we wanted to check if two polygons are colliding based upon their position and their size. This might be a good case for:

a$)$ A pure virtual function in Shape$2$D$,$ which Polygon and other classes must override

b$)$ A regular function in Shape$2$D$,$ which we do not expect to need to redefine in other classes

c$)$ A normal virtual function in Shape$2$D$,$ which may be overriden by some children but not all

d$)$ A normal function definition in main.cpp$,$ written by the client

Consider these options and write a comment explaining which choice you would make and why. If you would like to implement your choice for fun, you may! But that is not required. I $*$do$*$ have a correct answer in mind for which of these makes the most sense, but I can be persuaded by good reasoning!